演講訊息 TALKS

Abstract: Painlevé VI equation is a 2nd order nonlinear complex ODE. Hitchin in 1995 proved a beautiful theorem so called the Hitchin theorem which gives explicit expression for a class of solutions to PVI((1/8),((-1)/8),(1/8),(3/8)) (the Hitchin equation). In this talk, I will talk about a deep connection between Hitchin equation and mean field equation and apply it to study the smoothness of solutions to the Hitchin equation. Second, we will generalize the Hitchin theorem to the case PVI((1/2)(n+(1/2))²,((-1)/8),(1/8),(3/8)) where n∈N. As an important application of this generalization, we proved the pre-modular form obtained by Chai, Lin and Wang has simple zeros only and then confirm the Dahmen-Beukers conjecture.